(Mux founder here, but adding some additional community bits to the conversation) Probably unsurprisingly, the (honestly absurd world of) color is a pretty consistent topic among video engineers. Color theory is one of those areas that people working directly with it see it as a completely unsolved problem, and everyone else largely takes it for granted. This is a small sample size, but these are all talks just from…
There are definitely cases where it's clear what we (as browsers) are supposed to do, but some implementations have chosen to err on the side of user preference rather than correctness. I hope we can move that needle back towards "implement the specs". There's no good reason for any 601- or 709-marked content to display incorrectly in the year 2021.
Unfortunately, if you don't mark the videos, that's on you though. Fwiw Firefox generally does follow Chrome in inferring unmarked bt601/709 based on size: https://searchfox.org/mozilla-central/rev/1df3b4b4d27d413675...
Honestly I would rather issue warnings in these cases rather than silently guess.